MATS2300 Models in Financial Mathematics (5 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

The course gives an introduction to option pricing models for European and American options. Mainly the Cox-Ross-Rubinstein model is used, which provides a quick approach to several basic concepts in Finance and which is also used for numerical simulations.


The content of the course is:

  • geometric random walk,
  • arbitrage,
  • Fundamental Theorem of Asset Pricing,
  • riskneutral pricing of European and American options,
  • complete and incomplete markets
  • outlook to the Black-Scholes model

Learning outcomes

After the course, the student

  • is familiar with the basic concepts of finance (like arbitrage and risk neutral pricing)
  • can build a simple mathematical model for an asset price in discrete time and compute the fair price and hedge of an option
  • knows the Fundamental theorem of asset pricing
  • understands the Black-Scholes model and the connection to the above geometric random walk model
  • has developed learning skills by analyzing abstract mathematical models and the connection to their real life counterparts

Description of prerequisites

MATA280 Foundations of Stochastics

Recommended: Measure theoretic foundation of probability
(MATS260 Probability theory 1 or MATS112 Measure and Integration Theory 2)

Study materials

Lecture notes: C. Geiss. Financial Mathematics


D. Lamberton, B. Lapeyre: Stochastic Calculus Applied to Finance, 2008 (2nd ed), Chapman & Hall

N.H. Bingham & R. Kiesel: Risk-Neutral Valuation- Pricing and Hedging of Financial Derivatives (Springer); ISBN: SBN-13: 978-1584886266

Literature

  • D. Lamberton, B. Lapeyre: Stochastic Calculus Applied to Finance, 2008 (2nd ed), Chapman & Hall
  • N.H. Bingham & R. Kiesel: Risk-Neutral Valuation- Pricing and Hedging of Financial Derivatives (Springer); ISBN: SBN-13: 978-1584886266

Completion methods

Method 1

Evaluation criteria:
The grade of the course is determined by the points aquired in the exam and in the exercises.
Time of teaching:
Period 3
Select all marked parts

Method 2

Evaluation criteria:
The grade of the course is determined by the points aquired in the exam.
Select all marked parts
Parts of the completion methods
x

Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English
No published teaching